Depends on the OS you're using.
Filesize is not a Perl issue, as far as I know.
However, on a pre 2.4 linux Kernel, the file limit is 2GB.
BSD variants don't have this and can go significantly above this limit (far more than you'll get in a few weeks of plain text).
The same goes for NT and Novell. Not sure about the win 9x variants tho.
Actually file size can be a Perl issue. If you have Perl and compile without large file support, then you will be limited to 2 GB files, even if your OS can handle much larger. (Not that this matters to most people.)